On an Aitken type method

Authors

  • Ion Păvăloiu Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania
  • Emil Cătinaş Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat362-865

Keywords:

nonlinear equations, Aitken method
Abstract views: 332

Abstract

In this note we study the convergence of a generalized Aitken type method for approximating the solutions of nonlinear equations in \({\mathbb R}\). We obtain conditions which assure monotone convergence of the generated sequences. We also obtain a posteriori estimations for the errors.

Downloads

Download data is not yet available.

References

M.A. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, New York and London, 1980.

I. Păvăloiu, Solutions Equations by Interpolation, Dacia, Cluj-Napoca, 1981 (in Romanian).

I. Păvăloiu, Bilateral approximation of solution of equations by order three Steffensen-type methods, Studia Univ. "Babeş-Bolyai", Mathematica, LI (2006) no. 3, pp. 105-114.

I. Păvăloiu, and N. Pop, Interpolation and Applications, Risoprint, Cluj-Napoca, 2005 (in Romanian).

I. Păvăloiu, Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences, Calcolo, 32 (1995) nos. 1-2, pp. 69-82, https://doi.org/10.1007/bf02576543 DOI: https://doi.org/10.1007/BF02576543

I. Păvăloiu and E. Cătinaş, On a Steffensen type method, Proceedings of the Ninth International Symposion on Symbolic and Numeric Algoritms for Scientific Computing (SYNASC 2007), September 26-29, 2007, Timişoara, Romania, IEEE Computer Society, pp. 369-375. DOI: https://doi.org/10.1109/SYNASC.2007.83

B.A. Turowicz, Sur les derivées d'ordre superieur d'une fonction inverse, Ann. Polon. Math., 8 (1960), pp. 265-269, https://doi.org/10.4064/ap-8-3-265-269 . DOI: https://doi.org/10.4064/ap-8-3-265-269

Downloads

Published

2007-08-01

How to Cite

Păvăloiu, I., & Cătinaş, E. (2007). On an Aitken type method. Rev. Anal. Numér. Théor. Approx., 36(2), 173–176. https://doi.org/10.33993/jnaat362-865

Issue

Vol. 36 No. 2 (2007)

Section

Articles

License

Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.